A polyhedral reconstruction of a 3D object from a chain code and a low-density point cloud

Abstract The manipulation of 3D objects is becoming crucial for many applications, such as health, industry, or entertainment, to mention some. However, these 3D objects require substantial energy and different types of resources. With the goal of obtaining a simplified representation of a 3D object that can be easily managed, for example, for transmission, in some recent works, the authors associate low-density point clouds with a 3D object that simplifies the original 3D object. More precisely, given a 3D object in a polyhedral format, some authors associate a chain code and then use grammar-free context to obtain key points that give rise to several point clouds with different densities. In this work, we complete the cycle by developing a polyhedral reconstruction from an associated low-density point cloud and the chain code. The polyhedral reconstruction is crucial for handling 3D objects because it allows us to visualize them after they are efficiently compressed and transmitted. We apply our algorithms to well-known 3D objects in the literature. We use the Hausdorff and Chamfer distances to compare our results with the state-of-the-art proposals. We show how our proposed polyhedral reconstruction based on a helical chain code reconstructs a medical image represented or transmitted by slices into a 3D object in a polyhedral format, helping thus to mitigate and alleviate the management of 3D medical objects. The polyhedron that we propose provides better compression when compared with the original set of slices of a 3D medical object.